FILE PHOTO: MARISSA AMENDOLIA/THE HOYAIf the Hoyas win at Cincinnati on Saturday, they will receive a bye in the Big East tournament. If they lose to the Bearcats, they will be playing on day one at Madison Square Garden.

UPDATED: 3/4/11, 1:27 p.m.

It was not long ago that the Hoyas were in prime position to grab a double-bye in the Big East tournament. Now, with one game left in the regular season — and the entire 16-team league playing tomorrow — Georgetown needs a win in Cincinnati just to stay in the conference’s top eight.

True, had senior guard Chris Wright not gotten hurt, the argument can be made that the Hoyas would be 12-5 right now and still in serious contention for a top-four seed. Instead, they’ve lost three of four and sit at 10-7 and in eighth place behind West Virginia and Cincinnati — two other 10-7 clubs that own the tiebreaker over Georgetown.

The calendar has turned to March and seeding is up in the air for Head Coach John Thompson III’s team, both for the Big East tournament and the NCAA tournament. Let’s take a look at some of the Hoyas’ possible conference tournament seeding scenarios.

First, if Georgetown beats Cincinnati …

— Louisville beats West Virginia and Syracuse beats DePaul. Georgetown would get the No. 6 seed.

— West Virginia beats Louisville and Syracuse beats DePaul. Georgetown would get the No. 7 seed.

— Louisville beats West Virginia and DePaul beats Syracuse. Georgetown and Syracuse would be tied for the No. 5 seed at 11-7. Since their head-to-head is split at 1-1, the next tiebreaker would be common record against the top of the conference. Both teams are 0-1 against Pittsburgh, but Syracuse is 1-0 against Notre Dame and Georgetown is 0-1. Syracuse would get the No. 5 seed and Georgetown would get the No. 6 seed.

— South Florida beats St. John’s, Syracuse beats DePaul and Louisville beats West Virginia. Georgetown and St. John’s would be tied at 11-7. Since each team is 1-1 against each other, top-of-conference record comes into play. St. John’s is 1-0 against Pittsburgh, meaning the Red Storm would get the No. 5 seed and Georgetown would get the No. 6 seed.

— West Virginia beats Louisville and DePaul beats Syracuse. All three teams would be tied at 11-7. Since Syracuse is 2-1 against West Virginia and Georgetown, the Orange would get the No. 5 seed. West Virginia is 1-1 and would get the No. 6 seed. Georgetown is 1-2 and would get the No. 7 seed.

But if Georgetown loses to Cincinnati …

(There are a number of scenarios that could play out if the Hoyas lose and go to 10-8, so we’ll take a look at two of them.)

— We’ll start with the very complicated five-way tie scenario. If Cincinnati beats Georgetown, Louisville beats West Virginia, Marquette beats Seton Hall, Connecticut beats Notre Dame and Villanova beats Pittsburgh, five teams would finish 10-8. Connecticut would be 3-2 against the other four teams and would get the No. 7 seed, Marquette would be 1-3 against the other four teams and would get the No. 11 seed and Georgetown, West Virginia and Villanova would all be 2-2 against the other four teams. (Try to stay with me now). Each 2-2 team would subsequently be 1-1 against the other two 2-2 teams, moving us to the next tiebreaker: common record against the top of the conference. Villanova would be the only team to have a win over Pittsburgh, giving the Wildcats the No. 8 seed. Then due to the classic head-to-head tiebreaker, West Virginia would get the No. 9 seed, and Georgetown would get the No. 10 seed.

— Next, the slightly less complicated (and much more likely) three-way tie scenario: If Cincinnati beats Georgetown, Louisville beats West Virginia, Marquette beats Seton Hall, Pittsburgh beats Villanova and Notre Dame beats Connecticut, three teams would finish 10-8. Georgetown, West Virginia and Marquette would each be 1-1 against the other two teams, so the Hoyas would go to the top-of-conference tie-breaker. None of the three would have a win over Pittsburgh, but both West Virginia (1-0) and Marquette (1-1) would have wins over Notre Dame, making West Virginia the No. 7 seed, Marquette the No. 8 seed and Georgetown the No. 9 seed.

Finally, let’s assume things play out according to chalk (which often does not work in the Big East, but let’s try it anyway) …

— If each perceived “favorite” wins tomorrow and Georgetown also wins, Georgetown would get the No. 6 seed.

— If each perceived “favorite” wins tomorrow and Georgetown loses, Georgetown would get the No. 9 seed.

Figuring out where the dust has settled will be much more complicated if the Hoyas lose tomorrow, but as you can see — no matter what happens — some kind of tie-breaker will be used to finalize Big East tournament seeding. We haven’t gone through every possible scenario, but using the tie-breakers we employed, you can continue to play the “what if” game for win-loss combinations not found in this space.

But this much is certain: If the Hoyas beat Cincinnati, they will get a bye, and if they lose, they will play on day one of the tournament.